How do you move/migrate vSphere vCenter into the environment it is managing?

I have 3 hosts in a vSphere 5.5 Standard cluster running approx 40 VMs. They are running on shared storage (a SAN).

My vCenter is also a VM - running Windows 2012 - but it is running on an etirely different host (ESXi free version 5.1.0 799733) which, of course, is completely separate from the 3 main 5.5 hosts / cluster. It is running "VM Version 8" (also known as the "hardware version").

My question is: How do I go about migrating this vCenter VM into the cluster that it is managing, so that it becomes part of the "family"?

The perhaps most straight-forward way would probably be:

1) Shut down the vCenter VM
2) Export the vCenter from 5.1 as an ovf file
3) Connect directly to one of the 5.5 hosts with vSphere windows client (cannot connect to vCenter, coz it is shut down, and cant use web client either), and choose to "Deploy ovf template" (then selecting the vCenter ovf file)
4) Check that the vCenter VM's settings (especially network) are correct for operating from the "new" 5.5 host
5) Start up vCenter and hope everything falls into place

An alternative step 2 and 3 could also be:
2-alt) Copy the VM's files to a lun on the shared storage
3-alt) Connect directly to one of the 5.5 hosts, locate the vmx file on shared storage, and select "Add to inventory"

I'm just worried that the relocation will confuse vCenter (and/or the hosts) somehow, and it therefore will stop working. Also, there might be some kind of compatibility issue. Or something else that will trip me up.

Can somebody please point the way and/or alleviate my fears? Thanks in advance!

So, when the vCenter server starts up on the "new" ESXi 5.5 host, it will automatically "rediscover itself" as being one of the VMs on that 5.5 host? I don't need to do anything to facilitate that discovery?

Thank you very much for your insights. I have not yet performed the move, but I have no doubt that your directions are correct, so I hereby give you the points.

I do, however, have another very related question, if you could be so kind:

SHOULD I move the vCenter onto the cluster (/SAN) that it is managing? So far, that environment has been quite stable (knock on wood!), and the "outside" servers (upon which we are running the free ESXi version) are approaching the end of their warranty period. So - new hardware, or move "inside" - what's your take? This also goes for our 3Par SAN Processor, bty (also running on a VM on a free ESXi host).

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